Flow transport analysis method and system

ABSTRACT

A method and system for analyzing flow of a substance in a sewer system determines a first flow velocity at a first location and a second flow velocity at a second location. Using a processor, the travel time between the two locations is determined using only the flow velocities and a constant. The travel time may then be used to provide a substantially accurate determination of net flow between the two locations.

This application claims the benefit of U.S. application Ser. No.09/839,050, now U.S. Pat. No. 6,757,623 filed Apr. 20, 2001. The entirecontents of this prior application are incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates generally to flow monitoring systems in asewer network. More particularly, the present invention relates to amethod and system for determining the time corresponding to the flow ofa fluid from one point in a network to another without requiringdetailed information about the system, such as the distance between thetwo points or the number or character of sources between the points.

BACKGROUND OF THE INVENTION

Tools for the accurate measurement of flow in a sewer network are animportant resource for managers, mechanics, engineers, and regulators ofmunicipal and industrial sewer networks. Accurate measurements of flowbetween points, and an understanding of what flow is expected to occurat a downstream point based on upstream conditions, can helpdetermine—and to predict—when network problems such as leaks, breaks,clogs and other blockages and overflows may occur. They can also helpsystem engineers and designers understand when additional capacity mustbe built into the system, as well as to help them better manage anetwork with its existing capacity.

One key parameter that is measured in a sewer network is the net flowbetween two or more points. At a basic level, the volume of flow at adownstream location minus the volume of flow at an upstream location isconsidered to be the net flow between the two locations. The downstreamlocation volume is typically higher than that of the upstream locationunder normal conditions, as discharge sources, rainwater inflow andinfiltration, and/or other sources may introduce wastewater into thenetwork between the upstream and downstream locations. If the net flowbetween the two locations decreases below what is expected, or if netflow becomes negative, the network manager should investigate todetermine whether a leak, break, clog, or overflow is occurring.

However, the above-described general calculation of net flow does notconsider that it takes time for a particular flow element to travel fromthe upstream location to the downstream location, nor does it considerthat such time may vary. Thus, because of the “travel time,” by the timethat a flow reaches a downstream location from an upstream location, theconditions at the upstream location may have become significantlydifferent due to changes in input volumes, changes in weatherconditions, or any number of conditions. Thus, the traditional way ofcalculating net flow is not desirable because it does not account fortravel time or variations in travel time.

Sewer network managers have tried to compensate for the above-describedproblem in two ways. The first way is to use a larger number ofmonitoring points in the network, so that conditions are not likely tosignificantly change during the time that it takes wastewater to flowfrom one monitor to the next. However, flow monitors can be veryexpensive to purchase and costly to maintain. Thus, this solution is notdesirable because it is not cost-effective, and it is oftencost-prohibitive. In addition, the solution still does not account forthe travel time between the monitors that are installed.

The second way is to perform detailed modeling of travel time, based onvolumes of network design specifications and flow data. Such modelingexercises are time-consuming, costly, and only provide a snapshot of ananticipated travel time that matches the conditions under which themodeling occurred.

Thus, if a method and system for determining travel time in a sewernetwork were available that could determine the travel time in realtime, using a small number of monitors and relatively little input data,significant cost savings would result, and sewer network managers wouldbe better able to manage, predict conditions, anticipate designrequirements, and respond to problems in their networks.

Accordingly, it is desirable to provide an improved method and systemfor analyzing flow in a sewer network that includes the real-timederivation of the time that it takes for a flow to travel between pointsin the network.

SUMMARY OF THE INVENTION

It is therefore a feature and advantage of the present invention toprovide an improved method and system for analyzing flow in a sewernetwork that includes the real-time derivation of the time that it takesfor a flow to travel between points in the network.

In accordance with a preferred embodiment of the present invention, amethod of analyzing flow of a substance in a sewer network includes thesteps of collecting first data representative of a first flow velocityof a substance at a first location, as well as collecting second datarepresentative a second flow velocity of the substance at a secondlocation. In a preferred embodiment, the method also includestransmitting, via at least one communications link, the first data andsecond data to a processor. The processor determines a travel timecorresponding to travel of the substance between the first location andthe second location using only the first data, the second data, and aconstant. Preferably the processor does not require additional datarelating to the sewer network or the substance.

Optionally, the method also includes the steps of detecting a first flowvolume at the first location at a first time and detecting a second flowvolume at the second location at a second time. The second time is afunction of the first time and the travel time. The option also includestransmitting the first flow volume and the second flow volume to aprocessor. The processor determines a net flow corresponding to adifference between the second flow volume and the first flow volume.

Optionally, the determining step comprises divides the constant byeither a sum or an average of the first data and the second data.

Optionally, the constant corresponds to or is determined by historicflow volume data for the first location and historic flow volume datafor the second location over multiple time increments. As used herein,the word “historic” does not imply any particular age, and can includethe immediate past, even as close as a previous hour, minute, or second,as well as longer periods. To derive the constant, the method includesdeveloping a distribution of first flow volume data from the first flowmonitor over a period of time and a distribution of second flow volumedata from the second flow monitor over a period of time. The constantcorresponds to a goodness of fit test performed on the distributions.

As an additional option, the processor is integral with a flow meterthat is located at either the first location or the second location.

In accordance with another embodiment of the present invention, a systemfor analyzing flow of a substance between a first location and a secondlocation, includes a first meter capable of detecting a first flowvelocity at a first location and a second meter capable of detecting asecond flow velocity at a second location. The first meter and thesecond meter are in communication with a processor, and the processor isprogrammed to derive a travel time of a flow from the first location tothe second location using the first flow velocity, the second flowvelocity, and a constant. In a preferred embodiment of the presentinvention, no additional data relating to the flow or the locations arerequired.

Optionally, the first meter is also capable of detecting a first flowvolume at the first location at a first time, the second meter is alsocapable of detecting a second flow volume at the second location at asecond time. The second time corresponds to a sum of the first time andthe travel time, and the processor is further programmed to determine anet flow based on the difference between the second flow volume and thefirst flow volume.

Optionally, the first location and the second location are locationswithin a sewer network. As a further option, the processor may beintegral with the first or second meter.

In accordance with another embodiment of the present invention, a methodof analyzing flow of a substance in a sewer network includes the stepsof using multiple upstream flow meters to collect upstream flow volumedata points corresponding to each upstream flow meter over a period oftime, using a downstream flow meter to collect a downstream flow volumedata point, and determining a travel time corresponding to travel of asubstance between an upstream location corresponding to one of theupstream flow meters and a downstream location, the downstream locationcorresponding to the downstream flow meter, using the plurality ofupstream flow volume data points, the downstream flow volume data point,and a constant, without requiring additional data relating to the sewernetwork or the substance. Optionally, the method also includes the stepsof detecting a first flow volume at the upstream location at a firsttime, detecting a second flow volume at the downstream location at asecond time that is a function of the first time and the travel time,and determining a net flow corresponding to a difference between thedownstream flow volume and the upstream flow volume.

In accordance with another embodiment of the present invention, a methodof analyzing flow of a substance includes the steps of collecting afirst set of flow volume data at a first location over a multiple timeincrements, collecting a second set of flow volume data at a secondlocation over a corresponding number of time increments, identifying afirst distribution of the first set of flow volume data over time,identifying a second distribution of the second set of flow volume dataover time, identifying a constant corresponding to a relation of thefirst distribution and the second distribution, detecting a first flowvelocity at the first location, detecting a second flow velocity at thesecond location, and determining a transport time corresponding totransport of a substance from the first location using the first flowvelocity, the second flow velocity, and the constant, without requiringadditional data. Optionally, the method also includes using the firstflow meter at a first time, to detect an upstream flow volume, using thesecond flow meter at a second time being the sum of the first time andthe transport time to detect a downstream flow volume, and calculating anet flow corresponding to a difference between the downstream flowvolume and the upstream flow volume. Optionally, the relation in theidentifying step comprises a goodness of fit test.

In accordance with an additional embodiment of the present invention, amethod of analyzing flow of a substance in a sewer network includes thesteps of using a plurality of upstream flow meters to collect aplurality of sets of upstream flow volume data corresponding to eachupstream flow meter over a period of time, using a downstream flow meterto collect a set of downstream flow volume data over the period of time,identifying a plurality of upstream distributions corresponding to a setof upstream flow volume data over time, identifying a downstreamdistribution corresponding to the set of downstream flow volume dataover time, identifying a constant corresponding to a relation of theupstream distributions and the downstream distribution, detecting afirst flow velocity at an upstream location corresponding to one of theupstream flow meters, detecting a second flow velocity at a downstreamlocation corresponding to the downstream flow meter, and determining atransport time corresponding to transport of a substance from theupstream location to the downstream location using the first flowvelocity, the second flow velocity, and the constant, wherein thedetermining step does not require additional data. Optionally, themethod also includes using a first flow meter at the first upstreamlocation at a first time to detect an upstream flow volume, using thedownstream flow meter at a time corresponding to a sum of the first timeand the travel time to detect a downstream flow volume, and calculatinga net flow corresponding to a difference between the downstream flowvolume and the upstream flow volume. Optionally, the relation in theidentifying step comprises a goodness of fit test.

There have thus been outlined the more important features of theinvention in order that the detailed description thereof that followsmay be better understood, and in order that the present contribution tothe art may be better appreciated. There are, of course, additionalfeatures of the invention that will be described below and which willform at least part of the subject matter of the claims appended hereto.

In this respect, before explaining at least one embodiment of theinvention in detail, it is to be understood that the invention is notlimited in its application to the details of construction and to thearrangements of the components set forth in the following description orillustrated in the drawings. The invention is capable of otherembodiments and of being practiced and carried out in various ways.Also, it is to be understood that the phraseology and terminologyemployed herein, as well as the abstract included below, are for thepurpose of description and should not be regarded as limiting in anyway.

As such, those skilled in the art will appreciate that the concept andobjectives, upon which this disclosure is based, may be readily utilizedas a basis for the design of other structures, methods and systems forcarrying out the several purposes of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of the implementation of components of thepresent inventive system in a typical sewer network.

FIG. 2 is a flowchart that identifies the steps that a preferredembodiment of the present inventive method may follow along with anexemplary use for the travel time derived by the present invention.

FIG. 3 is a flowchart that identifies the steps that an additionalelement of a preferred embodiment of the present inventive method mayfollow.

FIG. 4 is a diagram illustrating how the results of the presentinvention may have application for use in the analysis of flow in anexemplary sewer network in which the measured flow may be moreaccurately understood when the travel time is taken into consideration.

FIG. 5 illustrates the exemplary flow measurements of FIG. 4 aftercompensation for travel time.

FIG. 6 illustrates an exemplary calculation of net flow when travel timeis not considered in the calculation.

FIG. 7 illustrates an exemplary calculation of net flow when travel timeis considered in the calculation.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

A preferred embodiment of the present invention provides a method andsystem for determining, in real time, the time that it will take for asubstance to flow from one point to another in a sewer network usingmeasured data corresponding to the flow, without requiring detailedinformation about the system, such as the distance or thecharacteristics of the sewer network. Once determined, this travel timemay be used to provide a more accurate measurement of net flow betweenthe two points, thus enhancing the ability of a system manager,engineer, or operator to detect discrepancies and/or unexpected networkconditions.

An illustration of a preferred embodiment of the present inventivesystem in an exemplary sewer system apparatus and method is illustratedin FIG. 1. Referring to FIG. 1, a sewer basin area 2 includes one ormore wastewater discharge sources such as 4, 6, 8, 10, and 12 thatdischarge wastewater 14, 16, 18, 20, and 22 into a sewer network 24. Thevolume of wastewater 26 in the sewer network increases as morewastewater is introduced into the network by the sources, and thewastewater flows through the network 24 toward a wastewater treatmentplant. A plurality of flow meters or monitors 30, 32, 34, and 36 arepositioned at various locations in the network 24. The meters may be ofany standard design or type that is capable of measuring flow velocity,either directly or indirectly by performing calculations on one or moremeasured parameters. Such a meter is described in, for example, U.S.Pat. No. 5,198,989, to Petroff; U.S. Pat. No. 4,630,474, to Petroff; andU.S. Pat. No. 4,397,191, to Forden. Preferably, the monitors are alsocapable of measuring flow volume, either directly or indirectly byperforming calculations on one or more measured parameters. Optionally,the monitors also may be capable of performing any other type ofmeasurement, such as temperature or depth of the flow.

The monitors preferably include communications capability such that datafrom at least two of the monitors may be delivered to a processordirectly. For example, as illustrated in FIG. 1, monitors 30, 32, 34 and36 may transmit the data that they collect via a wireless transmissionto a remote satellite 38, which relays the signal to a processor 28 suchas one located at the wastewater treatment plant. Optionally, theprocessor 28 may be located at any other location. For example, theprocessor may be located at one of the monitors, such as monitor 36illustrated in FIG. 1, in which case the transmission of data measuredby monitor 36 could be accomplished through direct or substantiallydirect delivery of a signal from a monitor sensor to the processor. Thewireless transmission to a satellite illustrated in FIG. 1 is only anexample of one form of communication that may be used. Any method orsystem that delivers the data collected by at least two monitors to aprocessor, such as a radio transmitter/receiver system, dial-in phonelines, Internet connectivity, or even direct wiring may be used.

The amount and the locations of the monitors, wastewater sources, andflow volumes illustrated in FIG. 1 are merely intended as illustrativeof an example of a sewer network that is equipped with the presentinvention. Any number and location of monitors and wastewater source maybe used. For example, the network may include only one upstream monitorand one downstream monitor. In the alternative, multiple upstreammonitors may be used with a downstream monitor.

The processor uses the flow velocity data collected by at least two ofthe monitors to determine the time that it takes a substance to travelbetween two points within the sewer network. The steps that theprocessor may perform to achieve this determination, along with theother steps taken by an exemplary method embodiment of the presentinvention, are illustrated in FIG. 2. Referring to FIG. 2, a first flowvelocity is collected 50 by a first flow meter. A second flow velocityis collected 52 by a second meter, and the first flow velocity and thesecond flow velocity are delivered 54, by direct wiring, radiotransmission, cellular transmission, Internet link, or any othercommunications medium to a processor. As noted above, the processor maybe separate from the monitors, or it may be integral with one of themonitors such that communication by such monitor is not required exceptto deliver the data from the sensor to the integral processor. Alsooptionally, each monitor may communicate via the same type ofcommunications medium, or different monitors may use different media.

After the data is received by the processor, the processor calculates 56the time that it took a substance in the network to travel from thelocation of the first monitor to the location of the second monitorusing only the first flow velocity, the second flow velocity, and apredetermined constant. Preferably, this calculation comprises dividingthe predetermined constant by the average of the first and second flowvelocities. Optionally, the calculation may comprise dividing thepredetermined constant by the sum of the first and second flowvelocities. This calculation may be performed at multiple times and/orlocations to identify multiple travel times.

The constant is a predetermined, sewer network-dependent value. It alsodepends upon the individual meters within the network for which a traveltime calculation is desired. The number of possible constants relates tothe number of monitors in the network. For example, if there are fourmonitors in a network in series, represented for the purpose ofdiscussion as monitors A, B, C, and D, there could be an A-B constant, aB-C constant, a C-D constant, an A-C constant, a A-D constant, a B-Dconstant, and a C-D constant. Not all such constants may apply, oradditional constants may apply, depending on the locations of themonitors in the network and in relation to each other. Although it ispossible that some of the constants could be the same, is not arequirement of the present invention that the constants be the same. Theconstant is preferably derived by studying the volume and travel timewithin the network over a period of time. Although travel times within anetwork will likely vary at different times and on different days asexternal factors such as flow volume, source input volume, and inflowand infiltration of rainwater occur, it has been surprisingly found thatthe constant will remain relatively unchanged. Preferably, the constantis determined and/or calibrated on a periodic basis, such as weekly,monthly, bimonthly, or any other period to account for changes to thesewer network over time.

FIG. 3 illustrates the steps that may be used to derive a constant inaccordance with a preferred embodiment of the present invention. First,a first flow meter collects 80 flow volume data at a first location overa plurality of time increments, such as ten-minute intervals, half-hourintervals, hourly intervals, daily intervals, or any interval. Only twosuch time increments are required, but the use of more time incrementswill likely result in a more accurate constant derivation. Similarly, asecond flow meter collects 82 flow volume data over a plurality of timeintervals that may or may not be the same as those for the first flowmeter measurements. A processor identifies, such as through ascatterplot or hydrograph such as the examples illustrated in FIG. 4, afirst distribution of the flow volume data from the first meter overtime 84 and a second distribution of the flow volume data from thesecond meter over time 86. The first distribution and the seconddistribution are then compared, using a “best fit” or “goodness of fit”test, to arrive at the constant that most closely results in a best fitbetween the distributions. The goodness of fit test may be any commonlyused goodness of fit test, such as the Kolmogorov-Smirnov test. thePearson's chi-square test, or any other such test. Preferably, the testis the Pearson's goodness of fit test and the constant is the Pearson'scorrelation coefficient.

Once calculated, the travel time can be used to calculate an accuratenet flow between the locations of the two monitors in the sewer system.Referring again to FIG. 2, the first and second monitors are used todetect a first flow volume 58 at the location of the first monitor and asecond flow volume 60 at the location of the second monitor. The firstflow volume is collected at a first time, and the second flow volume iscollected at a time that corresponds to the first time plus the traveltime. The flow volumes are then delivered 62 to a processor where theprocessor determines the net flow 64 between the first location and thesecond location by calculating the difference between the second flowvolume and the first flow volume. As with the delivery of volume data tothe processor in step 54, the delivery of volume data to the processorin step 62 may be by direct wiring, radio transmission, cellulartransmission, Internet link, or any other communications medium to aprocessor. Again, the processor may be separate from the monitors, or itmay be integral with one of the monitors such that communication by suchmonitor is not required except to deliver the data from the sensor tothe integral processor. In fact, the processor used in step 60 may bethe same processor as that used in step 54, or the processors may bedifferent processors. Also optionally, each monitor may communicate viathe same type of communications medium, or different monitors may usedifferent media.

FIG. 4 illustrates an exemplary application of the identification oftravel time to an analysis of net flow. FIG. 4 provides two exemplaryscatterplots of flow volume data over time. The solid line, representedby Q₁, is a plot of flow volume data from a hypothetical upstream flowmonitor in a hypothetical sewer network. The dotted line, represented byQ₂, is a plot of flow volume data from a hypothetical downstream flowmonitor in the same sewer network. The time between selected peaks orvalleys of the two scatterplots illustrates the travel time TT₁ or TT₂that it took the flow corresponding to the peak or valley of Q₁ totravel from the upstream monitor location to the downstream monitorlocation. In general, in any given network, monitor locations that arefurther apart will yield longer travel times, while monitor locationsthat are closer together will yield shorter travel times. Thus, traveltimes will vary at different times based on locations and networkconditions.

The differences in flow volume between the peaks and valleys of eachscatterplot will depend on the wastewater discharge sources, inflow andinfiltration, and other inputs into the sewer network. In addition, iffor example the peaks of a downstream scatterplot do not show anincrease, or if they show a smaller increase than is expected, whencompared to peaks on an upstream scatterplot, a sewer network managermay recognize that there is a problem within the sewer between themonitor locations. Such a problem may include, for example, a leak, asewer pipe break, a clog or other obstruction, or an overflow condition.

FIG. 5 illustrates the use of the scatterplots of FIG. 4, along with thetravel time, to calculate net flow between the hypothetical upstream anddownstream monitors. In FIG. 5, the downstream flow volume scatterplot,represented by Q₂, has been adjusted to compensate for the travel time.The net flow, represented by Q_(net), is a plot of the differencebetween Q₂ and Q₁. If a sharp change in the Q_(net) plot occurs, such achange may be indicative in a network problem, such as a leak, blockage,or overflow.

FIGS. 6 and 7 illustrate an example of how the calculation of traveltime can provide for a more accurate calculation of net flow. Referringto FIG. 6, exemplary upstream and downstream flow volume readings arerepresented at the top of the chart. The bottom of the chart illustratesa calculation of net flow as the difference between the downstream andupstream volumes. Because the net flow calculation in FIG. 6 does notaccount for travel time, the net flow calculation varies widely, andeven may be negative at times. FIG. 7, however, illustrates the effectof an adjustment of the upstream and/or downstream flows to compensatefor travel time. Thus, the net flow is a smoother line and is morerepresentative of actual conditions. This allows sewer network managersto more accurately detect variations in net flow that may result fromactual network problems. The data used in FIGS. 6 and 7 are merelyintended to illustrate an example of the application of the presentinvention, and are any number of variations are available depending uponthe actual data that is collected.

The many features and advantages of the invention are apparent from thedetailed specification, and thus, it is intended by the appended claimsto cover all such features and advantages of the invention which fallwithin the true spirit and scope of the invention. Further, sincenumerous modifications and variations will readily occur to thoseskilled in the art, it is not desired to limit the invention to theexact construction and operation illustrated and described, andaccordingly, all suitable modifications and equivalents may be resortedto, all of which may fall within the scope of the invention.

1. A method of analyzing flow of a substance in a sewer network,comprising: collecting first data representative of a first flowvelocity of a substance at a first location in a sewer network;collecting second data representative of a second flow velocity of thesubstance at a second location in the sewer network; and determining, bya processor, a travel time corresponding to the time it takes for thesubstance to travel between the first location and the second location,using the first data, the second data, and a constant.
 2. The method ofclaim 1 and further comprising: detecting a first flow volume at thefirst location at a first time; detecting a second flow volume at thesecond location at a second time, the second time being a function ofthe first time and the travel time; transmitting, via the at least onecommunications link, the first flow volume and the second flow volume toa processor; and determining by the processor, a net flow correspondingto a difference between the second flow volume and the first flowvolume.
 3. The method of claim 1 wherein the determining step requiresno addition data relating to the sewer network or the substance.
 4. Themethod of claim 1 wherein the determining step comprises dividing theconstant by a sum or an average of the first data and the second data.5. The method of claim 1 wherein the constant corresponds to historicflow volume data from a first flow meter for the first location andhistoric flow volume data from a second flow meter for the secondlocation, each of said historic flow volume data relating to a pluralityof time increments.
 6. The method of claim 1, further comprisingdeveloping a distribution of first flow volume data over a period oftime and a distribution of second flow volume data over the period oftime, and wherein the constant corresponds to a goodness of fit testperformed on the distributions.
 7. The method of claim 1 wherein theprocessor is integral with a flow meter that is located at the firstlocation or the second location.
 8. A system for analyzing flow of asubstance between a first location and a second location, comprising: afirst meter capable of detecting a first flow velocity at a firstlocation; and a second meter capable of detecting a second flow velocityat a second location; wherein the first meter and the second meter arein communication with a processor, and the processor is programmed toderive a travel time of a flow from the first location to the secondlocation using the first flow velocity, the second flow velocity, and aconstant
 9. The system of claim 8 wherein the first meter is alsocapable of detecting a first flow volume at the first location at afirst time, the second meter is also capable of detecting a second flowvolume at the second location at a second time, the second timecorresponds to a sum of the first time and the travel time, and theprocessor is further programmed to determine a net flow based on thedifference between the second flow volume and the flow volume.
 10. Thesystem of claim 8 wherein the processor does not require additional datarelating to the flow or the locations.
 11. The system of claim 8 whereinthe first location and the second location are locations within a sewernetwork.
 12. The system of claim 8 wherein the constant corresponds tohistoric flow volume data from the first meter for the first locationand historic flow volume data from the second meter for the secondlocation, each of said historic flow volume data corresponding to aplurality of increments.
 13. The system of claim 8 wherein the processoris integral with the first or second meter.
 14. A method of analyzingflow of a substance between a first location and a second location,comprising: collecting a first set of flow volume data at a firstlocation over a plurality of time increments; collecting a second set offlow volume data at a second location over the plurality of timeincrements; identifying a first distribution of the first set of flowvolume data over time; identifying a second distribution of the secondset of flow volume data over time; identifying a constant correspondingto a relation of the first distribution and the second distribution;detecting a first flow velocity at the fast location; detecting a secondflow velocity at the second location; and determining a transport timecorresponding to a transport of a substance from the first locationusing the first flow velocity, the second flow velocity, and theconstant, wherein the determining step does not require additional data.15. The method of claim 14, further comprising: detecting, using thefirst flow meter at a first time, a downstream flow volume; detecting,using the second flow meter at a second time, a downstream flow volume,the second time corresponding to a sum of the first time and thetransport time, and calculating a net flow corresponding to a differencebetween the downstream flow volume and the upstream flow volume.
 16. Themethod of claim 14 wherein the relation in the identifying stepcomprises a goodness of fit test.
 17. A method of analyzing flow of asubstance in a sewer network, comprising: collecting, using a pluralityof upstream flow meters, a plurality of sets of upstream flow volumedata, each corresponding to each upstream flow meter over a period oftime; collecting, using a downstream flow meter, a set of downstreamflow volume data over the period of time; identifying a plurality ofupstream distributions, each corresponding to a set of upstream flowvolume data over time; identifying a downstream distributioncorresponding to the set of downstream flow volume data over time;identifying a constant corresponding to a relation of the upstreamdistributions and the downstream distribution; detecting a first flowvelocity at a upstream location; detecting a second flow velocity at adownstream location corresponding to the downstream flow meter; anddetermining a transport time corresponding to transport of a substancefrom the upstream location to the downstream location using the firstflow velocity, the second flow velocity, and the constant, wherein thedetermining step does not require additional data.
 18. The method ofclaim 17 further comprising: detecting, using a first flow meterselected from the plurality of upstream flow meters at a first time, anupstream flow volume; detecting, using the downstream flow meter at asecond time, a downstream flow volume, the second time corresponding toa sum of the first time and the travel time; and calculating a net flowcorresponding to a difference between the downstream flow volume and theupstream flow volume.
 19. The method of claim 18 wherein the upstreamlocation corresponds to a location of one of the plurality of upstreamflow meters.
 20. The method of claim 17 wherein the relation in theidentifying step comprises a goodness of fit test.